Thomson Mass Spectrograph which is used to measure atomic masses of various isotopes in a gas :

Thomson mass spectrograph is used to measure atomic masses of various isotopes in a gas. This is done by measuring q/m of singly ionized positive ions of the gas. The positive ions are produced in the bulb at the left-hand side. These ions are accelerated towards cylindrical cathode C.

Some of the positive ions pass through the fine hole in the cathode. This fine ray of positive ions is subject to electric field E and magnetic field B and then allowed to strike a fluorescent screen or photographic plate placed just before the screen (not shown in figure). The positive ions produced near the anode are accelerated through a greater distance and thus have more kinetic energy and velocity. The different positive ions have different speeds. It can be shown that all positive ions having the same q/m, fall on the screen or photographic plate forming a parabolic trace. By changing the direction of B the other side of the parabola can be obtained.

It is found that separate isotopes forms separate parabola. Thus the number of parabolas (figure) given the number of isotopes in the gas taken in the bulb. Some ions after coming out of the cathode get neutralize and continue to move in a straight line. The impinge at the vertex of the parabola, forming a dark spot on the photographic plate.

The electric field and magnetic field are parallel to each other. However, the electric force and the magnetic force are perpendicular to each other. The deflection (upwards) due to the electric field alone as observed on the screen is .

$\displaystyle Y = \frac{q E L D}{m u^2}$

While the deflection (side ways) due to the magnetic field alone is

$\displaystyle X = \frac{q B L D}{m u}$

Eliminating u, we notice that when both E and B are present, then X – Y coordinates of the deflection are related by

$\displaystyle X^2 = \frac{B^2 L D}{E} (\frac{q}{m} ) Y$

For a given spectrograph B , L , D , E are constants , then

$\displaystyle X^2 = K (\frac{q}{m}) Y $

Note :

(1) Thus all positive ions having charge to mass ratio (q/m) lie on a parabola. Higher is the velocity, lower is the value of Y and X. In principle only those positive ions for which velocity is infinite can reach the origin O.

(2) Thus, infact, the trace does not extend upto origin O (vertex of the parabola). Since the highest velocity positive ions are those which originate near anode, the parabola’s lower end is due to high velocity ions, low velocity ions are far away from the vertex on the parabolic trace.

(3) To determine m_{1}/m_{2} ratio of isotopic masses, one draws a horizontal line on the parabolic trace (see figure). Thus Y is same for the two traces. Then the ratio m_{1}/m_{2} is found to be (use X^{2} = K (q/m) Y).

$ \displaystyle \frac{m_1}{m_2} = \frac{(AB)^2}{(CD)^2} $

where AB = 2X_{2} and CD = 2X_{1} in the figure. The heavier isotope lie on the inner parabolic trace while the lighter isotope is on the outer parabolic trace. The q/m is large for the outer parabola (m small) while q/m is small for the inner parabola. Thomson, using this spectrograph, discovered the isotopes of the neon.

Drawbacks:

(i) The resolving power of Thomson spectrograph is poor.

(ii) The parabolas are thick (diffused) as such it is difficult to accurately measure the distances AB and CD.

(iii) Since the positive ions are spread over a parabolic trace, the intensity is weak as such isotope having a little abundance may not be able to form a detectable parabolic trace.

(iv) If the positive ions before striking the screen (photographic plate) collide with atoms of the gas in the spectrograph tube, they will diffuse the parabolic trace and may also give rise to false parabolic traces.

(v) The relative abundance of the isotopes is estimated by intensity of the parabolic traces.